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We study the effect of the sigma(600) and a_1(1260) resonances in the rho^0 -> pi^+ pi^- gamma decay, within the meson dominance model. Major effects are driven by the mass and width parameters of the sigma(600), and the usually neglected contribution of the a_1(1260), although small by itself, may become sizable through its interference with pion bremsstrahlung, and the proper relative sign can favor the central value of the experimental branching ratio. We present a procedure, using the gauge invariant structure of the resonant amplitudes, to kinematically enhance the resonant effects in the angular and energy distribution of the photon. We also elaborate on the coupling constants involved.
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Proton-proton collision data recorded in 2011 and 2012 by the lhcb experiment, co-rres-pon-ding to an integrated luminosity of 3.0invfb, are a-na-lysed to search for the charmless ${B^0 to rho^0 rho^0}$ decay. More than 600 ${B^0 to (pi^+pi^-)(pi^+pi^-)}$ signal decays are selected and used to perform an amplitude analysis from which the ${B^0 to rho^0 rho^0}$ decay is observed for the first time with 7.1 standard deviations significance. The fraction of ${B^0 to rho^0 rho^0}$ decays yielding a longitudinally polarised final state is measured to be $fL = 0.745^{+0.048}_{-0.058} ({rm stat}) pm 0.034 ({rm syst})$. The ${B^0 to rho^0 rho^0}$ branching fraction, using the ${B^0 to phi K^*(892)^{0}}$ decay as reference, is also reported as ${BF(B^0 to rho^0 rho^0) = (0.94 pm 0.17 ({rm stat}) pm 0.09 ({rm syst}) pm 0.06 ({rm BF})) times 10^{-6}}$.
Theoretical errors in the extraction of alpha from B -> pi^+ pi^-, rho^+ rho^-, rho pi decays are usually given in terms of upper bounds on alpha_eff-alpha obtained from isospin or from SU(3) relations, where alpha_eff is measured through CP asymmetries. We show that mild assumptions about magnitudes and strong phases of penguin and tree amplitudes (|P/T| < 1 and |delta| < pi/2) in B -> pi pi and B -> rho rho, imply alpha_eff > alpha, thus reducing by a factor two the error in alpha. Similarly, the assumptions |p_+-/t_+-| < 1, |delta_-| < pi/2 <|delta_+| in B -> rho pi lead to a cancellation between two terms in alpha_eff-alpha. Current data support these conditions.
Using the close relationship between the low--energy constants of chiral perturbation theory and the chiral invariant interactions of the vector meson resonances with the pseudoscalar mesons, we investigate the process $rho^0 ra pi^+ pi^- gamma$. Compared with the contribution from the pure bremsstrahlung mechanism, we find an enhancement of the decay rate near the endpoint of the photon energy spectrum. Such a particular shape of the differential decay rate has indeed been observed experimentally and turns out to be an important confirmation of the theoretical concept of chiral vector meson dominance.
The ratio R_{eta}=Gamma(eta -> pi^+pi^-gamma)/Gamma(eta -> pi^+pi^-pi^0) has been measured by analyzing 22 million phi to eta gamma decays collected by the KLOE experiment at DAPhiNE, corresponding to an integrated luminosity of 558 pb^{-1}. The eta to pi^+pi^-gamma proceeds both via the rho resonant contribution, and possibly a non-resonant direct term, connected to the box anomaly. Our result, R_{eta}= 0.1856pm 0.0005_{stat} pm 0.0028_{syst}, points out a sizable contribution of the direct term to the total width. The di-pion invariant mass for the eta -> pi^+pi^-gamma decay could be described in a model-independent approach in terms of a single free parameter, alpha. The determined value of the parameter alpha is alpha = (1.32 pm 0.08_{stat} +0.10/-0.09_{syst}pm 0.02_{theo}) GeV^{-2}
We report the measurement of the ratio $Gamma(eta to pi^+pi^-gamma)/Gamma(eta to pi^+pi^-pi^0)$ analyzing a large sample of $phi to eta gamma$ decays recorded with the KLOE experiment at the DA$Phi$NE $e^+ e^-$ collider, corresponding to an integrated luminosity of 558 pb$^{-1}$. The $eta to pi^+pi^-gamma$ process is supposed to proceed both via a resonant contribution, mediated by the $rho$ meson, and a non resonant direct term, connected to the box anomaly. The presence of the direct term affects the partial width value. Our result $R_{eta}=Gamma(eta to pi^+ pi^- gamma)/Gamma(eta to pi^+ pi^- pi^0)= 0.1838pm 0.0005_{stat} pm 0.0030_{syst}$ is in agreement with a recent CLEO measurement, which differs by more 3 $sigma$ from the average of previous results.
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